Question

spiral review problems 10 - 11: here is polygon q. 10. what is the area of polygon q? 11. lola drew a scaled copy of polygon q using a scale factor of 2. what is the area of lolas polygon? explain your thinking.

Explanation:

Step1: Count full - squares and partial - squares

Count the full - unit squares inside polygon Q and combine partial squares to form whole squares. There are 6 full - unit squares and 4 half - unit squares.

Step2: Calculate area of polygon Q

The 4 half - unit squares are equivalent to 2 full - unit squares. So the area of polygon Q, $A_Q=6 + 2=8$ square units.

Step3: Recall the relationship between areas of similar polygons

If the scale factor of two similar polygons is $k$, the ratio of their areas is $k^{2}$. Here, $k = 2$.

Step4: Calculate area of Lola's polygon

Let $A_1$ be the area of polygon Q and $A_2$ be the area of Lola's polygon. We know that $\frac{A_2}{A_1}=k^{2}$. Since $A_1 = 8$ square units and $k = 2$, then $A_2=A_1\times k^{2}=8\times2^{2}=8\times4 = 32$ square units.

Answer:

1. 8 square units
2. 32 square units. The area of similar polygons is related by the square of the scale factor. Since the scale factor is 2, the area of the new polygon is 4 times the area of the original polygon. The original polygon has an area of 8 square units, so the new polygon has an area of 32 square units.